The group (F4 x F2) rtimes F_infinity, which is not finitely generated, is shown to admit an infinite minimal sofic shift, answering Question 7.18(ii) of Doucha, Melleray and Tsankov.
Generically there is but one self homeomorphism of the cantor set
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Minimal sofic shift on a group that is not finitely-generated
The group (F4 x F2) rtimes F_infinity, which is not finitely generated, is shown to admit an infinite minimal sofic shift, answering Question 7.18(ii) of Doucha, Melleray and Tsankov.